A broad assessment of the damage caused by disclosure of documents on classified intelligence programs has concluded that the former National Security Agency contractor who claimed responsibility for the leaks probably obtained dozens of other sensitive files, U.S. officials said Thursday.

The disclosure came as NSA and FBI officials came under new pressure from senior lawmakers to defend the agency’s interpretation of a law that it has used to sweep up the phone records of millions of U.S. citizens, and to declassify material to support NSA Director Keith B. Alexander’s assertion that the surveillance programs have helped to thwart “dozens” of terrorist attacks.

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An exchange between Rep. Louie Gohmert, R-Texas, and FBI Director Robert Mueller grew heated during a hearing of the House Judiciary Committee on FBI oversight Thursday.

Read all of the stories in The Washington Post’s ongoing coverage of the National Security Agency’s surveillance programs.

The early findings by investigators evaluating the scope of the breach appear to bolster former NSA contractor Edward Snow­den’s claims that he made off with additional classified files that have yet to be exposed. Snowden, who has sought refuge in Hong Kong, said he has documents showing extensive U.S. cyber-intrusions worldwide.

U.S. counterintelligence teams “believe that he has more,” said a U.S. official briefed on the status of the investigation. He said the NSA is “going through a major auditing” of materials to which Snow­den had access, seeking answers about how he was able to obtain a classified Foreign Intelligence Surveillance Court order and other records that should have been beyond his reach as a systems administrator.

U.S. officials are “worried that the disclosures will lead to a degradation over time of the effectiveness of the programs,” said the official, who spoke on the condition of anonymity because the assessment is ongoing.

The leaks about NSA surveillance activities have triggered a polarizing debate over the legal basis and effectiveness of programs that have swept up data on millions of U.S. citizens and been hailed as critical in preventing multiple terrorist attacks.

Sens. Mark Udall of Colorado and Ron Wyden of Oregon, Democratic members of the Senate Intelligence Committee who have been critical of the NSA’s activities, challenged Alexander’s claims that “dozens” of attacks have been avoided as a result of the programs.

“We have not yet seen any evidence showing that the NSA’s dragnet collection of Americans’ phone records has produced any uniquely valuable intelligence,” the lawmakers said in a statement Thursday. Contrary to Alexander’s assertion, they said classified information they have reviewed suggests that “all of the plots that he mentioned appear to have been identified using other collection methods. The public deserves a clear explanation.”

The Foreign Intelligence Surveillance Court order leaked by Snowden and subsequent disclosures indicate that the NSA has been collecting “metadata,” which includes the numbers, locations and durations, on billions of phone calls in the United States over the past seven years. Alexander and others have emphasized that the data contain no names and that the NSA can’t listen to the contents of those communications without additional permission from the court.

Lawmakers who support the program pushed the NSA to quickly declassify information about intercepted plots as well as about the safeguards the agency employs to protect U.S. citizens’ privacy. But even supporters have offered conflicting characterizations of the programs’ successes.

Rep. C.A. Dutch Ruppersberger (Md.), the ranking Democrat on the House Intelligence Committee, emerged from a closed-door briefing with Alexander on Thursday and said the leaks have damaged critical intelligence gathering programs that have “thwarted 10 possible terrorist attacks.”

Rep. Mike Rogers (R-Mich.), the committee chairman, then stepped forward to say that the number “far exceeds 10.” Rogers defended the collection of data on Americans, saying, “If you’re going to connect the dots on a 9/11-style event . . . you have to have dots in the box in order to connect.”

U.S. officials have so far identified two plots that they say the NSA programs helped to disrupt: a planned suicide bombing on the New York City subway system and a plot to attack a Danish newspaper by a Pakistani American, David C. Headley, who was arrested in 2009 for his role in a deadly attack the year before in Mumbai.

After a separate briefing attended by 47 members of the Senate, Sen. Dianne Feinstein (D-Calif.) indicated that the NSA is expected to declassify materials on those and other plots early next week. She said the process has been painstaking because Alexander “wants to be exact” with the data presented to the public.

“We’ll make an assessment based” on what Alexander presents, said Feinstein, chairman of the Senate Intelligence Committee. But she also indicated that lawmakers are already planning new legislation that would bar contractors such as Snowden from “handling highly classified technical data.”

The House and Senate hearings were part of a series of appearances on Capitol Hill by senior Obama administration officials to defend and explain the surveillance programs explosed by the leaks.

FBI Director Robert S. Mueller III was asked repeatedly during a House Judiciary Committee hearing to explain how the Foreign Intelligence Surveillance Act, which serves as the basis for the controversial NSA programs, allowed the agency to collect so much data on Americans who are under no legal suspicion.

The law “fails to impose a meaningful limit on the government’s ability to collect this type of information,” said Rep. John Con­yers Jr. (D-Mich.). “If every call is relevant, then the relevant standard we enacted into law has little practical meaning.”

Mueller’s response did little to clarify the administration’s position, centering instead on its effectiveness as a rationale. He said the data gathered by the NSA “may be relevant in the future, has been relevant in the past, and its collection in this matter thereby satisfies the requirement for relevance, according to the court.”

Mueller provided little information on the FBI’s pursuit of Snowden, the 29-year-old former CIA employee and NSA contractor, except to say that the bureau is “taking all necessary steps to hold this person responsible for these disclosures.”

Snowden’s whereabouts have been unclear since he checked out of a Hong Kong hotel two days ago, but he has indicated that he will seek asylum and fight extradition to the United States.

Since coming forward Sunday as the source of the NSA leaks, Snowden has alluded to additional U.S. national security secrets that he is prepared to disclose. In an interview in Hong Kong with the South China Morning Post, Snowden said the United States has conducted massive hacking operations against hundreds of Chinese targets since 2009. The newspaper said he had presented “unverified documents” describing those hacking operations.

After scouring Snowden’s employment records and computer access logs, U.S. officials believe he smuggled files from classified networks to which he had access as a systems analyst.

Snowden’s decision to flee to Hong Kong and his disclosures about alleged U.S. cyber operations against the Chinese have raised some suspicions of ties to that government. Rogers said, “We’re going to make sure that there’s a thorough scrub of what his China connections are.”

Other U.S. officials said no evidence has surfaced to substantiate those concerns.

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